Some Equivalence Theorem of the Continuity and Completeness of the System of Real Numbers
Jing Zhang · Journal of Beijing Union University · 2009
The definition of real numbers based on taking decimal as the jumping-off place,and on this basis,the monotone convergence theorem was proved.Some theorems describing the continuity and completeness of the system of real numbers were summarized,such as monotone convergence theorem,supremum(infimum) theorem,boundary point theorem,Dedekind cut theorem,Khinchin theorem,theorem of nested interval,principle of the point of accumulation,Heine-Borel theorem,Bolzano-Weierstrass theorem,Cauchy convergence criterion.